=(x-5y)(5x-6y)

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Solution for =(x-5y)(5x-6y) equation: 


Simplifying
0 = (x + -5y)(5x + -6y)

Multiply (x + -5y) * (5x + -6y)
0 = (x(5x + -6y) + -5y * (5x + -6y))
0 = ((5x * x + -6y * x) + -5y * (5x + -6y))

Reorder the terms:
0 = ((-6xy + 5x2) + -5y * (5x + -6y))
0 = ((-6xy + 5x2) + -5y * (5x + -6y))
0 = (-6xy + 5x2 + (5x * -5y + -6y * -5y))
0 = (-6xy + 5x2 + (-25xy + 30y2))

Reorder the terms:
0 = (-6xy + -25xy + 5x2 + 30y2)

Combine like terms: -6xy + -25xy = -31xy
0 = (-31xy + 5x2 + 30y2)

Solving
0 = -31xy + 5x2 + 30y2

Solving for variable 'x'.
Remove the zero:
31xy + -5x2 + -30y2 = -31xy + 5x2 + 30y2 + 31xy + -5x2 + -30y2

Reorder the terms:
31xy + -5x2 + -30y2 = -31xy + 31xy + 5x2 + -5x2 + 30y2 + -30y2

Combine like terms: -31xy + 31xy = 0
31xy + -5x2 + -30y2 = 0 + 5x2 + -5x2 + 30y2 + -30y2
31xy + -5x2 + -30y2 = 5x2 + -5x2 + 30y2 + -30y2

Combine like terms: 5x2 + -5x2 = 0
31xy + -5x2 + -30y2 = 0 + 30y2 + -30y2
31xy + -5x2 + -30y2 = 30y2 + -30y2

Combine like terms: 30y2 + -30y2 = 0
31xy + -5x2 + -30y2 = 0

Factor a trinomial.
(-5x + 6y)(x + -5y) = 0


Subproblem 1
Set the factor '(-5x + 6y)' equal to zero and attempt to solve:

Simplifying
-5x + 6y = 0

Solving
-5x + 6y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6y' to each side of the equation.
-5x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
-5x + 0 = 0 + -6y
-5x = 0 + -6y
Remove the zero:
-5x = -6y

Divide each side by '-5'.
x = 1.2y

Simplifying
x = 1.2y

Subproblem 2
Set the factor '(x + -5y)' equal to zero and attempt to solve:

Simplifying
x + -5y = 0

Solving
x + -5y = 0

Move all terms containing x to the left, all other terms to the right.

Add '5y' to each side of the equation.
x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
x + 0 = 0 + 5y
x = 0 + 5y
Remove the zero:
x = 5y

Simplifying
x = 5y
Solution
x = {1.2y, 5y}

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